Another simulation we performed is without initial magnetic field but with the Biermann battery effect. The induction equation is modified by adding an additional battery term[1]}:
\(\frac{\partial \bf {B}}{\partial t} & = & \nabla \times (\bf {v} \times \bf {B}) + \nabla \times (\frac{c \nabla p_e}{n_e e}) \\& = & \nabla \times (\bf {v} \times \bf {B}) + \frac{c m_H}{e} \frac{1}{1+\chi } \nabla \times (\frac{p}{\rho })\) 
